## Related questions with answers

Two small children, Daniel and Christine, were playing a game to see who would be the first to reach the door. The children started the game by standing 20 meters away from the door, and then they each alternated doing the following:

i. Daniel moved one-half the distance between himself and the door on each move.

ii. Christine moved 1 meter toward the door on each move.

(a) How far was each child from the door after the first move?

(b) After four moves, was Daniel or Christine closer to the door? Show your work.

(c) Daniel thought that the game was unfair because he would never reach the door. Explain why his statement is correct or incorrect.

Solution

Verified**a)** We know that Daniel moved one-half the distance between himself and the door on each move. Since on the first move the distance between Daniel and the door is 20 meters, he moved $\frac{20}{2}=10$ meters and he is $10$ meters from the door.

On the other hand, we know that Christine moved 1 meter toward the door on each move. So she moved 1 meter on the first move and she is $19$ meters from the door.

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